Dick Cheney himself said in 2011 “he didn’t have any problem with” same-sex marriage.

Mr Cheney and his wife Lynne released a statement today saying they had sought to deal with the issue privately “and we are pained to see it become public”.

They said their daughter had “always believed in the traditional definition of marriage” but “always treated her sister and her sister’s family with love and respect”.

Clearly aware of the risk that conservative hardliners would use that fact against Liz Cheney, they added: “Compassion is what is called for, even when there is disagreement about such a fundamental matter and Liz’s many kindnesses shouldn’t be used to distort her position”.

Mr Cheney, who served for eight years under former President George W Bush, has long been loathed by American liberals, but on the issue of equal marriage he has become an unexpected progressive, angering conservatives by announcing in 2000 that he would not oppose it.